# Basic Geometric Constructions

**The simplest geometric construction is the duplication of a given length.**
**Step 1: To duplicate the length of a given straight line segment AB, put the compass point on point A and open it to point B.**

**Step 2: Draw a straight line L of convenient length. Mark point A near one end. Without changing the compass setting, put the compass point on point A and mark point B.**

**The exact length of the given line segment AB has been transferred to line L.**

**The next construction is to draw the perpendicular bisector of a given line segment. This is simply a line which is perpendicular to segment AB and passes through it's midpoint.**

**Step 1: Put the compass point on point A and open it to more than half the length of segment AB. Draw an arc through the segment as shown.**

**Step 2: Without changing the compass setting, draw a second arc by putting the compass point on point B. The two arcs will intersect at two points as shown.**

**Step 3: Draw line XY through the two points where the arcs intersect. This is the perpendicular bisector of segment AB.**

**The next construction has to do with angles. Given an arbitrary angle, draw a line which divides (bisects) the angle into two equal angles.**

**Step 1: Open the compass to a convenient length. Put the compass point on point A and draw an arc through the given angle.**

**Step 2: Put the compass point on point B and draw an arc as shown.**

**Step 3: Without changing the compass setting, put the compass point on point C and draw another arc as shown.**

**Step 4: Draw a straight line XY through point A and the point where the two arcs intersect. This is the angle bisector.**